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This paper deals with global synchronization problem of multiple discrete-time Markovian jump memristor-based neural networks (DTMJMNNs) with mixed mode-dependent delays via a novel event-triggered impulsive coupling control (ETICC). The parameters of the multiple DTMJMNNs and the mixed time delays (both discrete and distributed delays) switch randomly according to a Markov chain. In the ETICC strategy, the controller does not work all the time, but only works at impulse instants determined by specific events. In particular, the coupling matrix can be non-Laplacian. By using the Lyapunov stability theory, linear matrix inequalities (LMIs), and the Kronecker product, some sufficient conditions for global synchronization of multiple DTMJMNNs under the event-triggered strategy are derived. Two examples are presented to test the validity of the theoretical analysis results. [ABSTRACT FROM AUTHOR]

In this paper, a novel class of quaternion-valued memristive neural networks (QVMNNs) that considers both the spatial factor and Markov jump phenomenon is proposed, the finite/fixed-time anti-synchronization (F/FTAS) of which is investigated. It is worth mentioning that the considered master and slave systems are assumed to jump along two inconsistent Markov chains, which is a first attempt at the issue of the anti-synchronization of Markovian systems and may be more realistic than most existing Markovian systems’ models. Then, a suitable feedback controller is designed, such that the error system can be finite/fixed-time stable. Moreover, by integrating algebraic inequality technologies and Lyapunov theory, a new F/FTAS theorem can be obtained for the proposed systems. Finally, this paper provides two examples, so that the rationality, superiority, and practical value of the main results can be illustrated. [ABSTRACT FROM AUTHOR]

Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the finite-time synchronization of a class of inertial neural networks with time delays. Without applying some finite-time stability theorems, which are widely applied to studying the finite-time synchronization for neural networks, by constructing two Lyapunov functions and using integral inequality method, two sufficient conditions on the finite-time synchronization for a class of inertial neural networks with time delays are derived. Considering that the method and research results of the finite-time synchronization are different from some existing works, this paper extends the works on the finite-time synchronization of neural networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global nonfragile Mittag–Leffler synchronization and the global synchronization in finite time for fractional-order discontinuous neural networks, where activation functions are discontinuous at 0, or modeled as a local Hölder functions with the nonlinear growth property in a neighborhood of 0. First, two lemmas concerned with the convergence with respect to an absolutely continuous function are developed. Second, a new property, which introduces an inequality of the fractional derivative for the variable upper limit integral with respect to the nonsmooth integrable function, is presented and applied in the synchronization results’ analysis. In addition, under the fractional Filippov differential inclusion framework, by utilizing the Lur’e Postnikov-type Lyapunov functional, nonsmooth analysis method, and the convergence properties developed in this paper, the synchronization conditions are derived in the form of linear matrix inequalities. Moreover, the upper bound of the setting time for the global nonfragile synchronization in finite time is calculated accurately. Finally, two illustrations are presented to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with exponential stabilization for a class of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes. [ABSTRACT FROM AUTHOR]

This paper deals with modeling and simulation of a new family of two-terminal devices fabricated with vanadium dioxide material. Such devices allow realization of very compact relaxation nano-oscillators that can be connected electronically to form arrays of coupled oscillators. Challenging applications of oscillator arrays include the realization of multiphase signal generators and massively parallel brain-inspired neurocomputing. In the paper, a circuit-level model of the vanadium dioxide device is provided which enables extensive electrical simulations of oscillator systems built on the device. The proposed model is exploited to explain the dynamics of vanadium dioxide relaxation oscillators as well as to accomplish a robust parameter design. Applications to the realization of voltage-controlled oscillators and of multiphase oscillator arrays are illustrated. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of adaptive exponential synchronization in mean square for a new neural network model with the following features: 1) the noise is characterized by the Lévy process and the parameters of the model change in line with the Markovian process; 2) the master system is also disturbed by the same Lévy noise; and 3) there are multiple slave systems, and the state matrix of each slave system is an affine function of the state matrices of all slave systems. Based on the Lyapunov functional theory, the generalized Itô’s formula, $M$ -matrix method, and the adaptive control technique, some criteria are established to ensure the adaptive exponential synchronization in the mean square of the master system and each slave system. Moreover, the update law of the control gain and the dynamic variation of the parameters of the slave systems are provided. Finally, the effectiveness of the synchronization criteria proposed in this paper is verified by a practical example. [ABSTRACT FROM PUBLISHER]

This paper focuses on the design of a pinning sampled-data control mechanism for the exponential synchronization of directed coupled reaction-diffusion neural networks (CRDNNs) with sampled-data communications (SDCs). A new Lyapunov–Krasovskii functional (LKF) with some sampled-instant-dependent terms is presented, which can fully utilize the actual sampling information. Then, an inequality is first proposed, which effectively relaxes the restrictions of the positive definiteness of the constructed LKF. Based on the LKF and the inequality, sufficient conditions are derived to exponentially synchronize the directed CRDNNs with SDCs. The desired pinning sampled-data control gain is precisely obtained by solving some linear matrix inequalities (LMIs). Moreover, a less conservative exponential synchronization criterion is also established for directed coupled neural networks with SDCs. Finally, simulation results are provided to verify the effectiveness and merits of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, for the case of the asynchronous switching caused by that subsystem’s switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper from new perspectives discusses the global synchronization of multiple recurrent neural networks (MNNs) with time delays via impulsive coupling. A new concept (coupling strength) is introduced, it is a variable parameter and plays a key role on synchronization. The selection of coupling strength can bring more convenience to the design of the impulsive coupling controller. Four results are presented for the synchronization of MNNs with time delays by using impulsive coupling with the coupling gain and variable topology, where two results are dependent on topology and other two results are independent on topological connectivity. In our results, the effects of each NN, coupling topology, and coupling strength can be positive or negative role on synchronization. In addition, three examples are presented to test our results in the theory analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential synchronization of reaction–diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction–diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction–diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction–diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of sampled-data synchronization for Markovian neural networks with generally incomplete transition rates. Different from traditional Markovian neural networks, each transition rate can be completely unknown or only its estimate value is known in this paper. Compared with most of existing Markovian neural networks, our model is more practical because the transition rates in Markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors. In addition, the time-dependent Lyapunov–Krasovskii functional is proposed to synchronize drive system and response system. By applying an extended Jensen’s integral inequality and Wirtinger’s inequality, new delay-dependent synchronization criteria are obtained, which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay. Moreover, the desired sampled-data controllers are obtained. Finally, two examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper investigates drive-response synchronization of a class of neural networks with time-varying delays and discontinuous activations. Discontinuous state feedback controller and adaptive controller are designed such that the considered model can realize exponential complete synchronization. Moreover, the convergence rate is explicitly estimated when state feedback control is utilized. The obtained results are also applicable to neural networks with continuous activations since they are a special case of neural networks with discontinuous activations. Results of this paper improve corresponding ones which only quasi-synchronization can be achieved for neural networks with discontinuous activations. Finally, numerical simulations are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper considers generalized discrete-time inertial neural network (GDINN). By timescale theory, the original network is rewritten as a timescale-type inertial NN. Two different scenarios are considered. In a first scenario, several criteria guaranteeing the global exponential stability for the addressed GDINN are obtained based on the generalized matrix measure concept. In this case, Lyapunov function or functional is not necessary. In a second scenario, some inequality analytical and scaling techniques are used to achieve the global exponential stability for the considered GDINN. The obtained criteria are also applied to the global exponential synchronization of drive-response GDINNs. Several illustrative examples, including applications to the pseudorandom number generator and encrypted image transmission, are given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov–Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization issue of time-varying Markovian jump neural networks (NNs). The denial-of-service (DoS) attack is considered in the communication channel connecting master NNs and slave NNs. An observer is designed based on the measurements of master NNs transmitted over this unreliable channel to estimate their states. The deception attack is used to destroy the controller by changing the sign of the control signal. Then, the mixed-type attacks are expressed uniformly, and a synchronization error system is established using this function. A finite-horizon $l_{2}-l_\infty $ performance is proposed, and sufficient conditions are derived to ensure that the synchronization error system satisfies this performance. The controllers are then obtained by a recursive linear matrix inequality algorithm. At last, a simulation result to show the feasibility of the developed results is given. [ABSTRACT FROM AUTHOR]

This paper considers the tracking synchronization problem for a class of coupled reaction–diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples. [ABSTRACT FROM AUTHOR]

In network systems, a group of nodes may evolve into several subgroups and coordinate with each other in the same subgroup, i.e., reach cluster synchronization, to cope with the unanticipated situations. To this end, the leader-following practical cluster synchronization problem of networks of generic linear systems is studied in this paper. An event-based control algorithm that can largely reduce the amount of communication is first proposed over directed communication topologies. In the proposed algorithm, each node decides itself when to transmit its current state to its neighbors and how to update its controller according to the estimations of the states of it and its neighbors. Then, the Lyapunov method is utilized to perform the convergence analysis. It shows that the practical cluster synchronization can be ensured by choosing appropriate parameters no matter what kind of estimation for the state is applied. Furthermore, the Zeno behavior is also excluded for each node under some mild assumptions. Besides, three kinds of common estimations for the states including zero-order hold model, first-order approximate model, and high-order model-based estimations are, respectively, analyzed from the perspective of the exclusion of Zeno behavior. Finally, the validity of the proposed algorithm is demonstrated, the effects of the concerned parameters are simply presented, and the effects of the three estimations are also compared through several simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov–Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical multisynchronization and static multisynchronization problem for delayed coupled multistable neural networks with fixed and switching topologies. To begin with, a class of activation functions as well as several sufficient conditions are introduced to ensure that every subnetwork has multiple equilibrium states. By constructing an appropriate Lyapunov function and by employing impulsive control theory and the average impulsive interval method, several sufficient conditions for multisynchronization in terms of linear matrix inequalities (LMIs) are obtained. Moreover, a unified impulsive controller is designed by means of the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness of the presented impulsive control strategy. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization analysis and control problems for a class of nonlinear discrete-time stochastic complex dynamical networks (CDNs) consisting of identical nodes. The discrete-time stochastic dynamical networks under consideration are quite general that account for asymmetric coupling configuration, nonlinear inner coupling structures as well as nonidentical exogenous disturbances. By resorting to both the error bound and the synchronization probability, a notion ofquasi-synchronization in probabilityis first introduced to assess the synchronization performance of the addressed CDNs. An event-triggered pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in the control process while preserving the desired dynamical behaviors of the controlled networks. By using the Lyapunov function method and the stochastic analysis techniques, a general framework is established within which the problems of dynamics analysis and controller synthesis are solved for the closed-loop stochastic dynamical networks. Two numerical examples and their simulations are presented to illustrate the effectiveness and the usefulness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dissipativity and synchronization problems of a class of delayed bidirectional associative memory (BAM) neural networks in which neuron activations are modeled by discontinuous bivariate functions. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides and mixed delays via functional differential inclusions. The global dissipativity of the Filippov solution to the considered BAM neural networks is proven using generalized Halanay inequalities and matrix measure approaches. Second, to realize global exponential complete synchronization of BAM neural networks with multivariate discontinuous activations, discontinuous state feedback controllers are designed using functional differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov functional method. Finally, several numerical examples are provided to demonstrate the applicability and effectiveness of our proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates exponential stabilization of continuous-time dynamic systems (CDSs) via event-based impulsive control (EIC) approaches, where the impulsive instants are determined by certain state-dependent triggering condition. The global exponential stability criteria via EIC are derived for nonlinear and linear CDSs, respectively. It is also shown that there is no Zeno-behavior for the concerned closed loop control system. In addition, the developed event-based impulsive scheme is applied to the synchronization problem of master and slave memristive neural networks. Furthermore, a self-triggered impulsive control scheme is developed to avoid continuous communication between the master system and slave system. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed event-based impulsive controllers. [ABSTRACT FROM AUTHOR]

Without confines of the continuous-time domain, this paper addresses synchronization control problem of neural networks in the face of multiple proportional delays on general time scales. The idea to deal with proportional delays is to propose a class of $q$ -type allowable time scales on which we design an appropriate controller to achieve exponential synchronization based on a calculus theory on time scales and Lyapunov function/functional methods. It is shown that adopting properties of $q$ -type time scales is an effective approach to establish synchronization for the networks with proportional delays. This helps us to have insight into the synchronization problems on general intermittent time domain. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time synchronization issue of nonlinear coupled neural networks by designing a new switching pinning controller. For the fixed network topology and control strength, the newly designed controller could optimize the synchronization time by regulating a parameter $\alpha $ ( $0\leq \alpha <1$ ). The control law presented in this paper covers both continuous controllers and discontinuous ones, which were studied separately in the past. Some criteria are discussed in detail on how to shorten the synchronization time for the strongly connected networks. Finally, the results are generalized to any network topologies containing a directed spanning tree, and one numerical example is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from $M$ -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov–Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of global exponential lag synchronization of a class of switched neural networks with time-varying delays via neural activation function and applications in image encryption. The controller is dependent on the output of the system in the case of packed circuits, since it is hard to measure the inner state of the circuits. Thus, it is critical to design the controller based on the neuron activation function. Comparing the results, in this paper, with the existing ones shows that we improve and generalize the results derived in the previous literature. Several examples are also given to illustrate the effectiveness and potential applications in image encryption. [ABSTRACT FROM PUBLISHER]

This paper addresses the global \cal H\infty pinning synchronization problem for a class of directed networks with aperiodic sampled-data communications. Important yet challenging issues of how many and which nodes should be pinned for realizing global synchronization in a fixed directed network without external disturbances are first discussed. By using a combined tool from the input-delay approach and free-weighting matrices technique, some sufficient synchronizability conditions are then derived for such networks. Furthermore, a multi-step algorithm is designed to estimate the upper bound of the maximum allowable sampling intervals for achieving synchronization. Theoretical results are then extended to global \cal H\infty pinning synchronization in fixed and switched directed networks with external disturbances, showing that a finite \cal H\infty performance index can be guaranteed under some suitable conditions. Finally, numerical simulations are performed to demonstrate the effectiveness of the analytical results. [ABSTRACT FROM PUBLISHER]

This paper addresses the telecoordinated control of multiple robots in the simultaneous presence of asymmetric time-varying delays, nonpassive external forces, and uncertain kinematics/dynamics. To achieve the control objective, a neuroadaptive controller with utilizing prescribed performance control and switching control technique is developed, where the basic idea is to employ the concept of motion synchronization in each pair of master–slave robots and among all slave robots. By using the multiple Lyapunov–Krasovskii functionals method, the state-independent input-to-output practical stability of the closed-loop system is established. Compared with the previous approaches, the new design is straightforward and easier to implement and is applicable to a wider area. Simulation results on three pairs of three degrees-of-freedom robots confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential synchronization for master–slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( \mathcal X , \mathcal Y , \mathcal Z )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example. [ABSTRACT FROM AUTHOR]

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov–Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of global exponential synchronization for a class of general neural networks that contains discontinuous activation functions and mixed time delays. Functional differential inclusions and nonsmooth analysis theories are used as bases to design discontinuous controllers, such that the discontinuous neural networks can be exponential complete synchronized. This novel approach and its applicability to neural networks with continuous activations are also easily verified. Several numerical examples demonstrate the practicality and effectiveness of the design method. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization issue of coupled reaction–diffusion neural networks with directed topology via an adaptive approach. Due to the complexity of the network structure and the presence of space variables, it is difficult to design proper adaptive strategies on coupling weights to accomplish the synchronous goal. Under the assumptions of two kinds of special network structures, that is, directed spanning path and directed spanning tree, some novel edge-based adaptive laws, which utilized the local information of node dynamics fully are designed on the coupling weights for reaching synchronization. By constructing appropriate energy function, and utilizing some analytical techniques, several sufficient conditions are given. Finally, some simulation examples are given to verify the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time-varying delay. Due to the parameter mismatch phenomena existed in neural networks, the problem of quasi-synchronization is thus discussed by applying some impulsive control strategies. Based on the definition of average impulsive interval and the extended comparison principle for impulsive systems, some criteria for achieving the quasi-synchronization of neural networks are derived. More extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization. In addition, according to the extended formula for the variation of parameters with time-varying delay, precisely exponential convergence rates and quasi-synchronization errors are obtained, respectively, in view of different types impulsive effects. Finally, some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, an antisynchronization problem is considered for an array of linearly coupled reaction–diffusion neural networks with cooperative-competitive interactions and time-varying coupling delays. The interaction topology among the neural nodes is modeled by a multilayer signed graph. The state evolution of a neuron in each layer of the coupled neural network is described by a reaction–diffusion equation (RDE) with Dirichlet boundary conditions. Then, the collective dynamics of the multilayer neural network are modeled by coupled RDEs with both spatial diffusion coupling and state coupling. An edge-based adaptive antisynchronization strategy is proposed for each neural node to achieve antisynchronization by using only local information of neighboring nodes. Furthermore, when the activation functions of the neural nodes are unknown, a linearly parameterized adaptive antisynchronization strategy is also proposed. The convergence of the antisynchronization errors of the nodes is analyzed by using a Lyapunov–Krasovskii functional method and a structural balance condition. Finally, some numerical simulations are presented to demonstrate the effectiveness of the proposed antisynchronization strategies. [ABSTRACT FROM PUBLISHER]

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov–Krasovskii functionals and Jensen’s inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications. [ABSTRACT FROM AUTHOR]

This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov–Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen’s integral inequality and Wirtinger’s inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, the synchronization problem of master–slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller’s side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master–slave chaotic neural networks. Lastly, Chua’s circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results. [ABSTRACT FROM PUBLISHER]

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of synchronization of switched delayed neural networks with communication delays via event-triggered control. For synchronizing coupled switched neural networks, we propose a novel event-triggered control law which could greatly reduce the number of control updates for synchronization tasks of coupled switched neural networks involving embedded microprocessors with limited on-board resources. The control signals are driven by properly defined events, which depend on the measurement errors and current-sampled states. By using a delay system method, a novel model of synchronization error system with delays is proposed with the communication delays and event-triggered control in the unified framework for coupled switched neural networks. The criteria are derived for the event-triggered synchronization analysis and control synthesis of switched neural networks via the Lyapunov-Krasovskii functional method and free weighting matrix approach. A numerical example is elaborated on to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of exponential stability analysis and synchronization of discrete-time switched delayed neural networks. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time-delays. Benefitting from the delay partitioning method and the free-weighting matrix technique, the conservatism of the obtained results is reduced. In addition, the decay estimates are explicitly given and the synchronization problem is solved. The results reported in this paper not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results. [ABSTRACT FROM PUBLISHER]

This paper is on the design problem of global exponential adaptive synchronization for a class of stochastic complex dynamical networks. In the considered networks, the dynamics of each node are approximated by a neutral-type neural network. The stochastic disturbances are described in terms of Brownian motions. Different from the prior references, the coefficient matrix of the adaptive controller under consideration is an arbitrary matrix instead of an identity one. By using Lyapunov method and some properties of Kronecker product, a sufficient condition is proposed to ensure the dynamics of the considered network globally exponentially synchronize with the desired solution in the mean square sense. Some criteria for global exponential adaptive synchronization of complex dynamical networks with general nodes are further provided in forms of corollaries. In particular, the proposed criteria for network synchronization are in terms of linear matrix inequalities. Only two variables are used in each criterion and the variables are not inside of any Kronecker product. Hence, the conditions are easy to check. A numerical example is presented to show the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper focuses on network-based master-slave synchronization for delayed neural networks through a remote controller. The insertion of communication networks in a master-slave synchronization scheme inevitably induces network delays, packet dropouts and stochastic fluctuations. The data packets may be received with a different temporal order from that they are sent due to the fact that the network-induced delay is time-varying. A logic data processor and a logic zero order hold are proposed in the master-slave synchronization framework. Then an error system for the master system and the slave system is formulated. By combining a generalized Jensen integral inequality and a convex combination technique, some synchronization criteria are derived to ensure the mean-square global exponential synchronization of state trajectories for the master system and the slave system. The controller gain matrix is obtained by solving a minimization problem in terms of linear matrix inequalities using a cone complementary technique. As a special case in which only network-induced delays and packet dropouts are occurred in the signal transmission channels, some results are also presented. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies synchronization in an array of coupled neural networks with Markovian jumping and random coupling strength. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable and each node has an interval time-varying delay. By designing a novel Lyapunov functional, using some inequalities and the properties of random variables, several delay-dependent synchronization criteria are derived for the coupled networks of continuous-time version. Discrete-time analogues of the continuous-time networks are also formulated and studied. Some new lemmas are developed to obtain less conservative synchronization criteria of both continuous-time model and its discrete-time analogues. Numerical examples of both continuous-time system and its discrete-time analogues are finally given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Coupled local minimizers (CLMs) turn out to be a potential global optimization strategy to explore a search space, avoid overfitting and produce good generalization. In this paper, convergence properties of CLMs based on an augmented Lagrangian function in the context of equality constrained minimization, are studied. We first consider the augmented Lagrangian by taking the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints. Then we study an array of CLMs within the Lagrange programming network framework and analyze the local stability of CLMs using a linearization strategy. We further show that, under some mild conditions, global asymptotical stability of the unique equilibrium point of the network can be guaranteed. Afterwards, some sufficient conditions are presented to ensure the stability of synchronization between any two minimizers via a directed graph method. The results show that the CLMs usually can be synchronized if the penalty factors in the array of CLMs are chosen large enough. It is worth pointing out that CLMs possess the capability of global exploration in the search space and the advantage of faster running time on convex problems in comparison with most of the neural network approaches, which is also illustrated through two test functions and their numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, new results on the global synchronization of multiple recurrent neural networks (NNs) with time delays via impulsive interactions are presented. Impulsive interaction means that a number of NNs communicate with each other at impulse instants only, while they are independent at the remaining time. The communication topology among NNs is not required to be always connected and can switch ON and OFF at different impulse instants. By using the concept of sequential connectivity and the properties of stochastic matrices, a set of sufficient conditions depending on time delays is derived to ascertain global synchronization of multiple continuous-time recurrent NNs. In addition, a counterpart on the global synchronization of multiple discrete-time NNs is also discussed. Finally, two examples are presented to illustrate the results. [ABSTRACT FROM AUTHOR]